The recent observations of galaxy and dark matter clumpy distributions have provided new elements to the understating of the problem of cosmological structure formation. The strong clumpiness characterizing galaxy structures seems to be present in the overall mass distribution and its relation to the highly isotropic Cosmic Microwave Background Radiation represents a fundamental problem. The extension of structures, the formation of power-law correlations characterizing the strongly clustered regime and the relation between dark and visible matter are the key problems both from an observational and a theoretical point of view. We discuss recent progresses in the studies of structure formation by using concepts and methods of statistical physics.

The energetics of cerebral activity critically relies on the functional and metabolic interactions between neurons and astrocytes. Important open questions include the relation between neuronal versus astrocytic energy demand, glucose uptake and intercellular lactate transfer, as well as their dependence on the level of activity. We have developed a large-scale, constraint-based network model of the metabolic partnership between astrocytes and glutamatergic neurons that allows for a quantitative appraisal of the extent to which stoichiometry alone drives the energetics of the system. We find that the velocity of the glutamate-glutamine cycle ($V_{cyc}$) explains part of the uncoupling between glucose and oxygen utilization at increasing $V_{cyc}$ levels. Thus, we are able to characterize different activation states in terms of the tissue oxygen-glucose index (OGI). Calculations show that glucose is taken up and metabolized according to cellular energy requirements, and that partitioning of the sugar between different cell types is not significantly affected by $V_{cyc}$. Furthermore, both the direction and magnitude of the lactate shuttle between neurons and astrocytes turn out to depend on the relative cell glucose uptake while being roughly independent of $V_{cyc}$. These findings suggest that, in absence of ad hoc activity-related constraints on neuronal and astrocytic metabolism, the glutamate-glutamine cycle does not control the relative energy demand of neurons and astrocytes, and hence their glucose uptake and lactate exchange.

The large scale distribution of galaxies in the universe displays a complex pattern of clusters, super-clusters, filaments and voids with sizes limited only by the boundaries of the available samples. A quantitative statistical characterization of these structures shows that galaxy distribution is inhomogeneous in these samples, being characterized by large-amplitude fluctuations of large spatial extension. Over a large range of scales, both the average conditional density and its variance show a nontrivial scaling behavior: at small scales, r<20 Mpc/h, the average (conditional) density scales as 1/r. At larger scales, the density depends only weakly (logarithmically) on the system size and density fluctuations follow the Gumbel distribution of extreme value statistics. These complex behaviors are different from what is expected in a homogeneous distribution with Gaussian fluctuations. The observed density inhomogeneities pose a fundamental challenge to the standard picture of cosmology but it also represent an important opportunity which points to new directions with respect to many cosmological puzzles. Indeed, the fact that matter distribution is not uniform, in the limited range of scales sampled by observations, rises the question of understanding how inhomogeneities affect the large-scale dynamics of the universe. We discuss several attempts which try to model inhomogeneities in cosmology, considering their effects with respect to the role and abundance of dark energy and dark matter.